Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds

We establish second order estimates for a general class of fully nonlinear elliptic equations with gradient terms on almost Hermitian manifolds including the deformed Hermitian-Yang-Mills equation and the equation in the proof of Gauduchon conjecture by Székelyhidi-Tosatti-Weinkove. As applications, we also consider the existence of Monge-Ampère equation and Hessian equations.